I will discuss two lattice avatars of ’t Hooft anomalies. The first one involves an action of a symmetry group on observables of a 1d spin system. It is related to a generalization of the Lieb-Schultz-Mattis theorem. The second one concerns symmetries of gapped states of spin systems. I will argue that the Hall conductance and other topological invariants of symmetric gapped states can be interpreted as obstructions to localizing the symmetry even approximately.  Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarIn this joint talk we focus on some recent results on packings of identical hard spheres of diameter D on 2D- and 3D- lattices and graphs (a unit triangular lattice A2, a unit honeycomb graph H2, a unit square lattice Z2, a unit cubic lattice Z3). In particular, we will use connections with the algebraic number theory. Our results identify dense-packing configurations and their random « perturbations » (extreme Gibbs distributions) describing high-density « pure phases » of the hard-sphere lattice model of statistical mechanics. ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarThis talk presents a quantitative homogenization for non-gradient exclusion process. The main strategy roots from the quantitative homogenization theory developed by Armstrong, Kuusi, Mourrat and Smart, and was already implemented in the previous work by Giunti-Gu-Mourrat’ 22 in an interacting particle system without exclusion. The new challenges here come from the hard core constraint of the particle number and the curse of dimension, and I will explain how to overcome them by a new coarse-grained strategy.  As an application, our result can be integrated into the classical work Funaki-Uchiyama-Yau’ 96 and yield a quantitative hydrodynamic limit. This talk is based on a joint work with Tadahisa Funaki (BIMSA) and Han Wang (Qiuzhen College, Tsinghua University).========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarClassical spin models taking value in the circle are naturally dual to spin models taking value in the integers (on the dual graph). Unlike in the context of Ising/Potts models, this duality is only visible at the level of order-disorder operators, there are no bijections between the models (as far as we know). I will revisit these well known relations, and will argue how the continuous symmetry group of S^1 will help to prove different results for the spin model and dual height function model. Notably, I will show a type of Gaussian domination holds for the height function on any graph, I will mention how it can be used to prove the Berezinskii–Kosterlitz–Thouless transition and time permitting, I will present some other results. All is based on joint work with Marcin Lis.  ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarI will talk about the eigenvalue asymptotics of the Laplace-Beltrami operator for certain singular Riemannian metrics. This is motivated by the study of propagation of soundwaves in gas planets. It is joint work in progress with Yves Colin de Verdière, Maarten de Hoop and Emmanuel Trélat.========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

We use holography to study the large spin J limit of the spectrum of low energy states with charge Q under a U(1) conserved current in CFTs in d>2 dimensions, with a focus on d=3 and d=4. For Q=2, the spectrum of such states is known to be universal and properly captured by the long-distance limit of holographic theories, regardless of whether the CFT itself is holographic. We study in detail the holographic description of such states at Q>2, by considering the contribution to the energies of Q scalar particles coming from single photon and graviton exchange in the bulk of AdS; in some cases, scalar exchange and bulk contact terms are also included. For a range of finite values of Q and J, we numerically diagonalize the Hamiltonian for such states and examine the resulting spectrum and wavefunctions as a function of the dimension Δ of the charge-one operator and the central charges cT, cJ of the stress tensor and U(1) current, finding multiple regions in parameter space with qualitatively different behavior. We discuss the extension of these results to the regime of parametrically large charge Q, as well as to what extent such results are expected to hold universally, beyond the limit of holographic CFTs. We compare our holographic computations to results from the conformal bootstrap for the 3d O(2) model at Q=3 and Q=4 and find excellent agreement. Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire Laurent Schwartz — EDP et applications

Séminaire Laurent Schwartz — EDP et applications 

Seminar on Quantum Modularity and ResurgenceThe partition function of topological string theory is an asymptotic series in the topological string coupling and provides in a certain limit a generating function of Gromov-Witten (GW) invariants of a Calabi-Yau threefold. I will discuss how the resurgence analysis of the partition function allows one to extract BPS invariants of the same underlying geometry. I will further discuss how the analytic functions in the topological string coupling obtained by Borel summation admit a dual expansion in the inverse of the topological string coupling leading to another asymptotic series at strong coupling and to the notion of topological string S-duality. This S-duality leads to a new modular structure in the topological string coupling. I will also discuss relations to difference equations and the exact WKB analysis of the mirror geometry. This is based on various joint works with Lotte Hollands, Arpan Saha, Iván Tulli and Jörg Teschner as well as on work in progress.========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

The simplest topologically ordered phase in 2+1D is the deconfined phase of Z2 lattice gauge theory. There are two reasonably well-understood ways to exit the deconfined phase: the Higgs transition, where electric charge (the « e » anyon) condenses, and the confinement transition, where magnetic charge (the « m » anyon) condenses. However, we can also exit the deconfined phase via the self-dual line in the phase diagram, where there is a symmetry between « e » and « m ». What happens here is more mysterious. If this transition is continuous, it may be the simplest critical point with no useful continuum Lagrangian (as yet). After reviewing the formulation of the model as the statistical mechanics of membranes, I will describe clear Monte Carlo evidence for the continuity of the self-dual transition. I will sketch why it is not a conventional « Landau » critical point. Separately, I will use the membrane formulation to describe a very concrete and intuitive way of understanding the emergent higher-form symmetries which appear in part of the phase diagram (and which are the reason that the Higgs and confinement transitions can be understood using Landau theory, despite lacking local order parameters). Work with Andres Somoza and Pablo Serna (https://arxiv.org/abs/2012.15845 and https://arxiv.org/abs/2403.04025). Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarOn a finite connected graph, the product of the non-zero eigenvalues of the Laplacian counts the rooted spanning trees, according to a theorem often attributed to Kirchhoff (1847), or sometimes to Sylvester (1857). Among many generalisations of this classical result, those of Zaslavsky (1982), Forman (1993) and Kenyon (2011) state that when we twist the Laplacian by putting a sign or a phase, complex or quaternionic, on each edge, its determinant counts covering forests of unicycles, with appropriate weights. A common feature of all these results is that the random subgraphs naturally associated to each of these situations (uniform spanning trees and random covering forests of unicycles), seen as random subsets of the (finite) set of edges of the ambient graph, are determinantal point processes. I will present some results of an ongoing joint work with With Adrien Kassel (CNRS, ENS Lyon) in which we investigate further extensions of these results to the covariant Laplacian associated with an arbitrary unitary connection, that is, to the Laplacian twisted by a unitary matrix on each edge. In a first part, I will describe the classical results of Kirchhoff and Forman, then (from a perhaps slightly unorthodox point of view) determinantal point processes on finite sets, and explain what the ones have to do with the others. In a second part, I will describe the measures on Grassmannians that we introduced with Adrien Kassel, explain why they are relevant to the understanding of the twistes Laplacian, and finally describe, to the extent that we understand them, the new random objects that appear over a graph endowed with a unitary connection.========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Seminar on Quantum Modularity and ResurgenceThe talk will focus on quantum modularity relations satisfied by the $q$-Pochhammer symbol  $(q)_N = (1-q) … (1-q^N)$ at $q=exp(2 pi i x)$. These formulas can be interpreted as finite analogues of the usual modularity for the Dedekind eta-function. We’ll discuss certain aspects which come very handy upon summing over $N$. We’ll explain how these can be used, in the context of Kashaev’s invariant of hyperbolic knots, to prove, in a few cases, Zagier’s quantum modularity conjecture by means of what we currently know on the Volume Conjecture. This is based on joint work with Sandro Bettin.========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.